HTML injection into someone else's website?

Question

I've got a product that embeds into websites similarly to Paypal (customers add my button to their website, users click on this button and once the service is complete I redirect them back to the original website).

I'd like to demo my technology to customers without actually modifying their live website. To that end, is it possible to configure http://stackoverflow.myserver.com/ so it mirrors http://www.stackoverflow.com/ while seamlessly injecting my button?

Meaning, I want to demo the experience of using my button on the live website without actually re-hosting the customer's database on my server.

I know there are security concerns here, so feel free to mention them so long as we meet the requirements. I do not need to demo this for website that uses HTTPS.

More specifically, I would like to demonstrate the idea of financial bounties on Stackoverflow questions by injecting a Paypal button into the page. How would I demo this off http://stackoverflow.myserver.com/ without modifying https://stackoverflow.com/?

REQUEST TO REOPEN: I have reworded the question to be more specific per your request. If you still believe it is too broad, please help me understand your reasoning by posting a comment below.

UPDATE: I posted a follow-up challenge at How to rewrite URLs referenced by Javascript code?

UPDATE2: I discarded the idea of bookmarklets and Greasemonkey because they require customer-side installation/modification. We need to make the process as seamless as possible, otherwise many of get turned off by the process and won't let us pitch.

Answer 1

I would suggest to create a proxy using a HTTP handler.

In the ProcessRequest you can do a HttpWebRequest to get the content on the other side, alter it and return the adjusted html to the browser. You can rewrite the urls inside to allow the loading of images, etc from the original source.

public void ProcessRequest(HttpContext context)
{
  // get the content using HttpWebRequest
  string html = ...

  // alter it

  // write back the adjusted html
  context.Response.Write(html);
}